Jeremy Hunt has called for a better journey through the NHS for elderly, vulnerable people. Photograph: Neil Hall/PA

The health secretary has been told to stop making negative claims about the NHS after he said elderly patients are better known to accident and emergency staff than their local GPs.

Dr Clare Gerada, chair of the Royal College of General Practitioners, said that NHS was working well and there was "blatantly" no evidence for Hunt's claim.

Gerada criticised the health secretary after he said in a Daily Telegraph article that the new GPs' contract, introduced in 2004, had undermined the relationship between patients and GPs by abolishing the system of having a named doctor.

In the article, Hunt wrote: "We've got to a point where A&E staff know some patients better than their own GPs. Of course, GPs don't want it to be this way, and are themselves working harder than ever before. But sadly the 2004 contract changes undermined the personal link between them and their patients, as well as imposing a whole range of bureaucratic burdens."

Gerada told BBC Radio 4's Today programme: "I am sure Mr Hunt regrets saying emergency doctors know their patients better than their GPs because there is blatantly no evidence for that. But there is a need to look at how we treat and care for whole ranges of patients, including our elders."

The RCGP chair said that the NHS needed an extra 10,000 GPs, to help alleviate pressure on existing doctors. She said: "GPs are heaving under the workload. They don't stop at night. That is very disingenuous. It is not the fairies that do the night calls."

She said it was wrong to suggest that NHS was not working well. "It is working. It is working less well now since the massive cuts that we have seen and the enormous top-down reorganisation that we have just had. But the NHS was working and is still working. We need to stop sending the message out that the NHS is failing."

Hunt told Today that the government had plans for 2,000 extra GPs. But he pointed out that Keith Willett, professor of orthopaedic trauma surgery at Oxford, has said that 15 – 30% of A&E patients could be treated by their GP.

The health secretary said: "As a member of the public I would like the person who is the mainstay of my care in the NHS to be my GP. But contract changes made that very difficult. It undermined the personal link between GPs and the people on their lists by abolishing the idea of a named GP.

"People who have named GP are less likely to spend time in hospital. In certain cases, like the frequent flyers of the NHS, particularly some of the frail older people or some of the people with repeat problems, I think GPs would be much better at looking after those people."